Question

Hello, can you solve this question​

Answer 1

Given :

• Angle A = 42°
• Angle DCA = 14°
• AB = AC

This means that triangle is isosceles.

__________________________

To Find :

The value of Angle BCD

__________________________

Solution :

Given, AB = AC ,

so, this triangle is Isoceles

Hence, Angle ABC = Angle ACB = x

So, 42°+x+x = 180° (angle sum property)

$\tt{ \implies \: {42}^{ \circ} + 2x = 18 {0}^{ \circ} }$

$\tt{ \implies 2x = 1 {80}^{ \circ} - {42}^{ \circ} }$

$\tt{ \implies x = \frac{13 {8}^{ \circ} }{2} }$

$\implies \tt{x = 6 {9}^{ \circ} }$

Hence, Angle ABC = Angle ACB = 69°

So, Angle BCD = Angle ACB -14°

or, Angle BCD = 69°-14°

or, Angle BCD = 55°